MCQMediumJEE Main 2023 · 31 January, Shift 2Modulus & Argument

Mathematics Question from JEE Main 2023 · 31 January, Shift 2

The complex number z=i−1cos⁡π3+isin⁡π3z = \frac{i-1}{\cos \frac{\pi}{3} + i \sin \frac{\pi}{3}} is equal to:

  • A

    2(cos⁡5π12+isin⁡5π12)\sqrt{2} \left( \cos \frac{5\pi}{12} + i \sin \frac{5\pi}{12} \right)

  • B

    cos⁡π12−isin⁡π12\cos \frac{\pi}{12} - i \sin \frac{\pi}{12}

  • C

    2(cos⁡π12+isin⁡π12)\sqrt{2} \left( \cos \frac{\pi}{12} + i \sin \frac{\pi}{12} \right)

  • D

    2 i(cos⁡5π12−isin⁡5π12)\sqrt{2}\, i \left( \cos \frac{5\pi}{12} - i \sin \frac{5\pi}{12} \right)

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